In a recent paper published on Nature, Google researchers claim they programmed a quantum processor to perform a task that would require 10,000 years on a state-of-the-art classical supercomputer. Google's claim did not entirely persuade IBM researchers, who proposed an ideal simulation of the quantum task which, they argue, only requires 2.5 days on a classical computer and provides greater fidelity.
The task Google chose to demonstrate quantum supremacy consists in sampling the output of a pseudo-random quantum circuit, which produces a set of bit-strings with a certain probability distribution. This task has an immediate application for the generation of certifiable random numbers. Using their 53-qubit Sycamore processor, Google researchers showed sampling one instance of a quantum circuit one million times required 200 seconds.
The same task carried through using a simulation of the same quantum circuit run on a classical computer would take, say Google researchers, 10,000 years.
This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy for this specific computational task, heralding a much-anticipated computing paradigm.
Besides playing the role of a benchmark, the simulation on the classical computer was also used to demonstrate the correctness of the result produced by the quantum processor, as measured by its fidelity. The way Google set up the classical simulation was straightforward. Indeed, simulating a quantum computer is feasible in reasonable time for quantum circuits using up to 43 qubits. This is due to the possibility of simulating the 243 quantum states using a sufficiently large RAM memory. Once the limits of maximum available memory are reached, simulating a larger qubit number requires running the algorithm on a distributed system with a cost that inevitably, say Google researchers, grows exponentially. Furthermore, any future improvements in quantum simulation algorithms will be likely offset by hardware improvements on larger quantum processors, they say.
The relevance of Google's experiment is not only theoretical for its implications on quantum supremacy. In fact, fidelity is greatly affected by quantum gates error rates, which is a major issue in quantum computing since the lack of error correction techniques means noise can heavily affect measurements and induce errors. So, demonstrating the possibility of attaining high fidelity, i.e. low error rates, in a practical quantum processor is of fundamental importance to the future development of quantum computing. It also matters because of a number of a technical advances that were necessary for this experiment to work out successfully. In particular, the paper authors mention three fundamental breakthroughs: the development of fast, high-fidelity gates; a new technique to calibrate and benchmark the quantum processor based on cross-entropy; and the ability to accurately predict quantum information behaviour as it scaled to a larger system.
With the outcomes, Google researchers claim they have proved two distinct results: that a quantum processor can perform a task in a sufficiently large quantum space and with sufficiently low error rates; and that a computation task can be devised that is easy for a quantum processor and hard for a classical computer. Those two intermediate results are what led Google researchers to claim they proved quantum supremacy.
The second point is what IBM researchers are objecting to. In a second paper submitted to Quantum Physics, they show how secondary storage can be used to extend the range of quantum circuits that can be practically simulated on a classical system and proved their result using IBM Oak Ridge National Laboratories supercomputer. Specifically, they say, a Sycamore circuit with 53 and 54 qubits can be simulated with high fidelity in a matter of days.
When [Google researchers'] comparison to classical was made, they relied on an advanced simulation that leverages parallelism, fast and error-free computation, and large aggregate RAM, but failed to fully account for plentiful disk storage. In contrast, our Schrödinger-style classical simulation approach uses both RAM and hard drive space to store and manipulate the state vector.
In their paper, IBM researchers are also defending a more radical philosophical stance on quantum supremacy, though, claiming the term "quantum supremacy" is causing confusion due to its fundamental misinterpretation.
Quantum computers will never reign “supreme” over classical computers, but will rather work in concert with them, since each have their unique strengths.
IBM researchers are not the only ones critical of that term, as its original proponent, John Preskill, summarized in a recent article. One of the ways the use of that term is not doing a great service to quantum computing is pointedly highlighted by Preskill with reference to Google's successful experiment:
The catch, as the Google team acknowledges, is that the problem their machine solved with astounding speed was carefully chosen just for the purpose of demonstrating the quantum computer’s superiority. It is not otherwise a problem of much practical interest.
Others, though have been more positive. Speaking to the New York Times, Scott Aaronson, a computer scientist at the University of Texas at Austin who reviewed Google’s paper before publication, likened Google’s announcement to the Wright brothers’ first plane flight in 1903:
The original Wright flyer was not a useful airplane, but it was designed to prove a point. And it proved the point.
All in all, it seems it is definitely too early to say whether Google achievement will be recorded in the annals of quantum computing. What seems to be widely recognized, including by Preskill and IBM researchers, is that Google's achievement represents a pivotal step in the evolution of practical quantum computers, opening the way to the creation and use of noisy intermediate-scale quantum computers for more cogent applications.